We employ a stochastic dominance (SD) approach to derive a relative environmental degradation index across countries. The variables that are considered include countries' greenhouse gas (GHG) emissions, water pollution and the net forest depletion, as from the data set of the World Bank. A worst-case scenario index to measure environmental degradation across different countries and at different times is constructed applying a methodology that is based on multivariate comparisons of country panel data over various years and consistent tests for SD efficiency. The test statistics and the estimators are computed using mixed integer programming methods. It is found that in the worst-case scenario index, GHG emissions contribute the most (with a weight around 68%), net forest depletion contributes with around 30%, and water pollution contributes the least (with a weight around 2%). Our index can be a useful tool for policy making in conveying information on the environmental quality and a quick assessment of sustainable performance across countries and over time.